Here we have only treated pure gravity and thus to properly address the cosmological constant problem we should understand the situation when matter is coupled to gravity [1]}. Indeed, arguably there was never a cosmological constant problem in pure gravity since if we adopt dimensional regularisation only terms proportional to \(\rho _k\)  would renormalise \(\rho _k\)  and we can simply set \(\rho _k=0\) . What will remain true even in the presence of matter is that there is an inessential coupling related to a rescaling of the spacetime metric. This might shed new light on the cosmological constant problem [2]}.
